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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

A planet has a radius R₁ , and a satellite revolves around it in a circle of radius R₂ . The time period of revolution is T . Determine the acceleration due to the planet's gravitation at its surface.

Options

  1. A2 ^2 R₂^3 T^2 R₁^2
  2. B4 ^2 R₁^3 T^2 R₂^2
  3. C4 ^2 R₂^2 T^2 R₁
  4. D4 ^2 R₂^3 T^2 R₁^2

Correct answer

D. 4 ^2 R₂^3 T^2 R₁^2

Step-by-step solution

Let M be the mass of the planet. The acceleration due to gravity at the surface of the planet is given by g = GM R₁^2 . For a satellite revolving in a circular orbit of radius R₂ , the time period T is given by T = 2 R₂^3 GM . Squaring both sides, we get T^2 = 4 ^2 R₂^3 GM , which yields GM = 4 ^2 R₂^3 T^2 . Substituting this value of GM into the expression for g , we obtain g = 4 ^2 R₂^3 T^2 R₁^2 .

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